Probably some would judge me in a store. I do what works for myself and my children, and I provide limits and supervision. I am not perfect, but mostly it works out.
My kids have special needs, so I know a lot of folks judge us already, but we have to make adaptations in our lives to help them manage. We try not to take our kids shopping too much, but sometimes it is impossible to avoid it...and honestly, I know it is good practice for them.
My kids may walk in the store if they are holding onto the cart (or basket). I try to involve them in shopping or pushing the cart (with my help), which gives them something to focus on and means they are far less likely to start sensory-seeking screaming (which is deafening and can happen in an instant if I am not vigilant in providing them with a multitude of sensory inputs...which in the store includes opportunities to interact with their environment).
I sometimes send them ahead, further down an aisle, to find a food with which they are familiar. dd's walk, due to her special needs, is closer to a run, but if she is purposefully and truly running or if she is not being careful or courteous of others, then I treat it as true running. Occassionally this happens...they run inappropriately, which often results in time within the cart followed by a re-try later.
If nobody is in an aisle we are in, and the store is not crowded (so it is unlikely folks will be joining us in the aisle), I do let my kids run up and down the aisle or push the cart around a bit if they watch where they are going and don't go to the end of the aisle (in case anyone turns into the aisle with their cart). They know that this is a "special occassions" thing and they have to ask permission from me first.
We re-cart if and when necessary, if behavior takes a turn for the downside.
Occassionally folks have to slow down and wait patiently for a minute while my kids get some yogurt out of the dairy shelf, yes, but I slow down and wait patiently also while a woman, my elder, does the same just as slowly for mobility limitations. It's a give and take, interacting in this intergenerational world full of people with diverse needs and challenges.
Kids are growing, learning human beings, and the best way for them to learn is through hands-on experiences. By shopping outside of the cart, they learn and practice a variety of life skills, including but not limited to:
*Safety: following me closely, staying on the correct side of the aisle for traffic flow, watching carefully for carts and people as well as other hazards, etc.
*Patience: waiting in cue to get something off the shelf when someone else is getting something, or to make purchases.
*Courtesies: saying excuse me as needed, using words like please and thank you, not pushing the cart too close to others, letting others pass as needed, and so forth.
I say do what works best for your family, but just make sure to provide appropriate limits and supervision.